Unions of chainable continua with the fixed point property

We investigate the fixed point property for continua that are unions of chainable continua. We answer Question 2 of our paper [Fund. Math. 231 (2013)] by showing the fixed point property is additive for chainable continua. We additionally show that (i) various finite unions of chainable continua have the fixed point property, and (ii) infinite unions of chainable continua that are $1$-dimensional, upper semicontinuous clumps as defined by H. Cook have the fixed point property.